In our previous post, we concluded that air above the desert cools down by 10°C in the first hour after sunset because cold air descends slowly from above as the day's convection cycle comes to a stop. This explanation is not one of the several you will find on the web if you search for "Why does the desert get so cold at night?" These other explanations talk about dry air allowing heat to radiate away into space. But our calculations in Day and Night showed that the rate at which the Earth and its atmosphere radiate heat is barely adequate to cool the air by half a degree in ten hours, let alone ten degrees in one hour.
One of our readers points us to another night-time cooling phenomenon called "night inversion". According to this description, the air immediately above a forest can be 10°C cooler at night than the air 100 m up. In our explanation of the desert cooling, the cold air above the desert was still warmer than the air higher up, but in this case, the air above the forest is actually colder than the air higher up. We will conclude our Surface Cooling series by offering an explanation for nigh inversion also.
The first 100 m of the atmosphere has heat capacity 100 kJ/K/m2. The forest is a good black body, so it will radiate of order 100 W/m2 directly into space through a clear night sky. A leaf, being roughly 1 mm thick, and consisting mostly of water, has heat capacity roughly 4 kJ/K/m2. When it radiates 100 W/m2 it will tend to cool by more than 1°C every minute. It is the heat capacity of the air around it that will stop the leaf from freezing.
The forest leaves will set up a convection cycle in which air is cooled by the upper leaves, which are the ones radiating into space, and warmed by the surface of the Earth below. The air immediately above the forest will be sucked into this cycle, and the air immediately above that also, so that the very cold air of the tree-tops mixes slowly with the air ten to a hundred meters up, creating a layer of air that is colder and more dense than the air above. The convection cycle transports roughly 100 W/m2. Suppose that the mixing we describe causes 30 W/m2 to be removed from the heat capacity of the first 100 m of air. In that case, the average temperature of the first 100 m will drop by 5°C in six hours.
So we see that radiation by leaves held ten or twenty meters above the ground can cause the first hundred meters of the atmosphere to cool by several degrees compared to the air above, and so create a static, cold layer of air above the forest. If there is any wind, of course, the leaves will no longer need their convection cycle to keep them warm: the wind will warm them, and blow away any cold air as well. The night must be still for such inversion to take place, and air is more often still in a bowl or valley.
Our Surface Cooling posts have introduced us to the heat capacity of the atmosphere, and shown us that traditional explanations for cooling and warming may be unreliable. But we have no proof that it is an exchange of warm air for cold air that causes the sudden drop in temperature at sunset in the desert. Nor do we have any proof that a cold convection cycle in a forest causes night inversion. Both explanations are merely hypotheses. Any help devising experiments to test either hypothesis would be much appreciated. Our ideas so far, which involve helium balloons and battery-powered thermometers, appear impractical, not to mention expensive.